s143 nilas mandrup hansen.pdf

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Interaction between Seabed Soil and Offshore

Wind Turbine Foundations

PhDT

hesis

Nilas Mandrup HansenDCAMM Special Report No. S143

March 2012


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Interaction between Seabed Soil and

Offshore Wind Turbine Foundations

Nilas Mandrup Hansen

March 2012

Department of Mechanical EngineeringSection for Fluid Mechanics, Coastal and Maritime Engineering

Technical University of Denmark


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Published in Denmark byTechnical University of Denmark

Copyright c N. M. Hansen 2012All rights reserved

Section for Fluid Mechanics, Coastal and Maritime EngineeringDepartment of Mechanical EngineeringTechnical University of DenmarkNils Koppels Alle, Building 403, DK2800 Kgs. Lyngby, DenmarkPhone +45 4525 1411, Telefax +45 4588 4325E-mail: [email protected]: http://www.mek.dtu.dk/

Publication Reference DataHansen, N. M.Interaction between Seabed Soil and Offshore Wind Turbine FoundationsPhD ThesisTechnical University of Denmark, Department of Mechanical EngineeringDCAMM Special Report, no. S141March, 2012ISBN: 978-87-90416-80-5Keywords: Pile foundation, soil reaction modulus, COMSOL, Biots consolidation equations,

Experimental work, Liquefaction


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Preface

The present Ph.D. thesis is submitted as part of the requirement for obtain-ing the Ph.D. degree from the Technical University of Denmark. The Ph.D.has been conducted at the Department of Mechanical Engineering, Section

for Fluid Mechanics, Coastal and Maritime Engineering. The main supervi-sion was undertaken by professor B. Mutlu Sumer.

The present study is the result of contributions from many individuals.First and most importantly, I would like to thank Mutlu Sumer for sharinghis experience and wisdom. It has been an educational experience.

I would also like to give special thanks to co-supervisor professor JrgenFredse for useful discussions during the project, to associate professor OleHededal and Ph.D. student Rasmus Tofte Klinkvort for assistance withinthe field of geotechnics, to professor Dong-Sheng Jeng at Dundee Universityfor kindly providing the foundation of the numerical model, to Niels-ErikOttesen Hansen for his comments in relation to offshore windfarms and to

my colleague postdoc Niels Gjl Jacobsen for many enlightening discussionsduring the entire project.

Also I would like to thank the entire staff at the Section for Fluid Mechan-ics, Coastal and Maritime Engineering. Special thanks are given to the staffat the sections experimental lab facility, including the former colleagues Hen-ning Jespersen and Jan Larson for support during the experimental setup.

In addition, I would like to thank the Danish Council for Strategic Re-search (DFS)/Energy and Environment and the Technical University of Den-mark for providing the financial support, making this Ph.D. study possible.

And finally, I would like to thank my wonderful wife and daughter for theirpatience and encouragement, especially when times were hard, throughout

the past three years.

Kgs. Lyngby, March 2012

Nilas Mandrup Hansen

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Abstract

Today, monopiles are widely used as foundation to support offshore windturbines (OWT) in shallow waters. The stiffness of monopiles is one of theimportant design aspects. Field observations show that some monopiles, al-

ready installed in the field, behaves more stiff than predicted by the currentdesign recommendations. The present study addresses the pile/seabed in-teraction problem, related to the stiffness of the monopile by means of anumerical model and experimental investigations.

The numerical model is a 3D model. COMSOL Multiphysics, a finite-element software, is used to calculate the soil response. The model is based onthe Biot consolidation theory which involves a set of four equations, the firstthree equations describing the equilibrium conditions for a stress field, andthe fourth one, the so-called storage equation, describing the conservation ofmass of pore water with the seepage velocity given by Darcys law (Sumer andFredse, 2002, chap. 10). The constitutive equation for the soil consideredin the model is the familiar stress-strain relationship for linear poro-elasticsoils. The so-called no-slip boundary condition is adopted on the surface ofthe rocking pile.

The numerical model is validated against the laboratory experiments. Theexperimental setup includes a container (a circular tank with a diameter of2 m and a height of 2.5 m), and a stainless steel model pile (with a diameterof 20 cm). Coarse sand (d50= 0.64 mm) is used in the experiments.

Pore-water pressures, pile displacements and forces on the pile are mea-sured in the experiments. The pore-water pressure is measured at 12 pointsover a mesh extending 0.75 m in the vertical and 0.10 m in the radial direc-

tion (the measurement points closest to the pile being at 2 cm from the edgeof the pile), using Honeywell pressure transducers. The pile displacement ismeasured, using a conventional potentiometer, while the force is measuredwith a tension/compression S-Beam load cell.

The model, validated and tested, is used to calculate the soil response fora set of conditions, normally encountered in the field. The results are pre-sented in terms of non-dimensional p-y curves, obtained from the numericalsimulations. A parametric study is undertaken to observe the influence ofvarious parameters on the latter.

The parametric study shows that, for a given displacement, y, the soil

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resistance p, increases with increasing S, a non-dimensional parameter re-sponsible for generation and further dissipation of the pore-water pressure.

The parametric study also shows that, again for a given y, the soil resistanceincreases with decreasing bending stiffness of the pile, expressed in terms ofa non-dimensional quantitys. Finally, the soil resistance increases, when thenon-dimensional foundation depth decreases.


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Resume

I dag er monople brugt i vid udstrkning som fundament til offshore vind-turbiner opfrt i lavt vand. Et vigtigt aspekt i monoplens design er densstivhed. Feltmalinger har vist, at nogle monople, som allerede er installeret,

opfrer sig mere stift end forudset af den nuvrende design anbefaling. Dettestudie undersger problematikken omkring pl/havbunds interaktionen, re-lateret i forhold til stivheden af monoplen ved brug af en numerisk modelog eksperimentelle undersgelser.

Den numeriske model er en 3D model. COMSOL Multyphysics, som er etFinite Element program, er brugt til at beregne jordens respons. Modellen erbaseret pa Biots konsoliderings teori, hvilke involverer et st af fire ligninger,hvor de tre frste ligninger beskriver ligevgtsbetingelserne i et stress felt ogden fjerde, den sakaldte storage ligning, beskriver bevarelsen af porevand,hvor porevandets gennemstrmningshastighed er beskrevet ved Darcys lov(Sumer and Fredse, 2002, chap. 10). Den konstitutive ligning som er brugttil at beskrive jordens opfrsel er det velkendte spndings-tjningsforhold foren linear poro-elastisk jord. En no-slip betingelse er brugt som randbetingelsepa overfladen af den rokkende pl.

Den numeriske model er valideret imod eksperimentelle forsg. Den eksperi-mentelle forsgsopstning inkluderer en beholder (en rund beholder med endiameter pa 2 m og en hjde 2.5 m), og et rustfrit stalrr (med en diameterpa 20 cm). Groft sand (d50 = 0.64 mm) er blevet brugt i forsgene.

Porevandtrykket, plens flytning og krfterne pa plen blev malt i forsg-ene. Porevandtrykket er malt i 12 punkter over et net som udbreder sig0.75 m i vertikal retning og 0.10 m i horisontal retning (det ttteste malepunkt

var 2 cm fra plens overflade), ved brug af Honeywell tryk transducere.Plens flytning blev malt med et almindeligt potentiometer og kraften blevmalt med en trk/tryk lastcelle.

Modellen, nar den er valideret og testet, bruges derefter til at beregnejordens respons for en rkke betingelser, normalt mdt i felten. Resultaternebliver prsenteret i form af nogle dimensionslse p y kurver, udarbejdet pabaggrund af de numeriske simuleringer. Et parameter studie udfres for atobservere pavirkningen af forskellige parameter pa de fromtalte pykurver.

Parameterstudiet viser, at for en given flytning y, stiger jordens mod-standp med stigende S, en dimensionsls parameter ansvarlig for produktio-

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nen og yderligere spredningen af porevandtrykket. Parameterstudiet viseryderligere, igen for en givet flytning y, at jordens modstand stiger med

faldende bjningsstivhed af plen, udtrykt i form af en dimensionsls strrelses. Til sidst, jordens modstand ges, nar den dimensionslse funderingsdybdemindskes.


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Contents

Preface i

Abstract iii

Resume v

Nomenclature xi

1 Introduction 11.1 Statement of the Problem . . . . . . . . . . . . . . . . . . . . 11.2 Motivation of the Problem . . . . . . . . . . . . . . . . . . . . 11.3 Existing work . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 The Niche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 The Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6 Methodology and Terminology . . . . . . . . . . . . . . . . . 51.6.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . 51.6.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . 6

2 Numerical model. Biot Equations 92.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 The Pile . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 The Seabed . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Soil in a confined Domain . . . . . . . . . . . . . . . . 12

2.3.2 Soil in a unconfined Domain . . . . . . . . . . . . . . . 132.3.3 Pile Constraint . . . . . . . . . . . . . . . . . . . . . . 132.3.4 Pile displacement . . . . . . . . . . . . . . . . . . . . . 142.3.5 Free surface . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.6 Pile/soil Interface . . . . . . . . . . . . . . . . . . . . . 142.4 Assumptions and Limitations . . . . . . . . . . . . . . . . . . 142.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5.1 Features used in COMSOL . . . . . . . . . . . . . . . 152.5.2 Special Issue with Infinite Elements . . . . . . . . . . 162.5.3 Computing Reaction Forces . . . . . . . . . . . . . . . 16

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viii Contents

2.5.4 Discretization, Analysis type and Time-scheme . . . . 162.5.5 Hardware and Computational Time . . . . . . . . . . 17

3 Experimental Investigation of Pile-Soil Interaction 193.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.1 The Experimental Setup . . . . . . . . . . . . . . . . . 20

3.1.2 Pile Displacement . . . . . . . . . . . . . . . . . . . . 203.1.3 PWP Measurements . . . . . . . . . . . . . . . . . . . 22

3.1.4 Seabed preparation . . . . . . . . . . . . . . . . . . . . 273.1.5 Visualization . . . . . . . . . . . . . . . . . . . . . . . 28

3.1.6 Test Conditions . . . . . . . . . . . . . . . . . . . . . . 28

3.1.7 Data Treatment and Analysis . . . . . . . . . . . . . . 303.2 Soil Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 363.3.1 Coarse Sand . . . . . . . . . . . . . . . . . . . . . . . 36

Pore-water Pressure during cyclic Loading . . . . . . . 36Vertical Pore-water Pressure Distribution . . . . . . . 44

Pile Deflection under Cyclic Loading . . . . . . . . . . 463.3.2 Coarse Silt . . . . . . . . . . . . . . . . . . . . . . . . 48

Build-up of Pore-water Pressure . . . . . . . . . . . . 48Liquefaction . . . . . . . . . . . . . . . . . . . . . . . . 50

Pore-water Pressure Dissipation and Compaction Front 51

4 Model Validation 57

4.1 Wave-induced pore-water pressure under Progressive Waves . 574.1.1 Solution to the Biot Consolidation Equations for Finite

Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Solution for Saturated Soil . . . . . . . . . . . . . . . 60

Solution for Unsaturated Soil . . . . . . . . . . . . . . 604.1.2 Solution to the Biot Consolidation Equations for Infi-

nite Depth . . . . . . . . . . . . . . . . . . . . . . . . 62Solution for Saturated Soil . . . . . . . . . . . . . . . 63

Solution for Unsaturated Soil . . . . . . . . . . . . . . 64

4.2 Cyclic Motion of Monopile Foundation . . . . . . . . . . . . . 664.2.1 Model Geometry and Boundary Conditions . . . . . . 66

4.2.2 Input Parameters . . . . . . . . . . . . . . . . . . . . . 674.2.3 Time-Series Validation of Pore-water Pressure . . . . . 68

4.2.4 Model Tuning . . . . . . . . . . . . . . . . . . . . . . . 704.2.5 Vertical Distribution of Pore-Water Pressure . . . . . 71

4.2.6 Discussion of Mesh Size . . . . . . . . . . . . . . . . . 73

5 Numerical Model for Full-Scale Conditions 775.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.2 Non-Dimensional Quantities . . . . . . . . . . . . . . . . . . . 795.3 Model Geometry and Boundary Conditions . . . . . . . . . . 81


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Contents ix

5.4 Test Conditions and Input Parameters . . . . . . . . . . . . . 835.5 Computational Mesh . . . . . . . . . . . . . . . . . . . . . . . 85

5.6 Pile Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.7 Soil Resistance Distribution and Non-Dimensional p-y curves 895.8 Reaction Modulus Comparison . . . . . . . . . . . . . . . . . 985.9 Cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6 Conclusion 101

References 103

A Additional Data from the Coarse Sand Experiments. 109

B Constant Head Permeability Test (Coarse Sand) 111

C Soil Sampling - Coarse Silt 117

D Strain Gauge Calibration 119

E Coarse Soil Elastic- and Strength Properties 123

F Derivation of Eq. 5.13 129


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x Contents


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Nomenclature

The following nomenclature lists the symbols used in the report if not statedotherwise.

Greek Characters

Constant, typically 0.5 0.7 for sand

Compressibility of the pore fluid

Slope of the failure line (Appendix E)

Stress vector

Strain vector

Dimensionless parameter indication soil anisotropy and degree of sat-

uration

Boundary layer thickness (Sec. 4.1.2)

Combined wave and soil parameter (Sec. 4.1.1)

Length scale of diffusion (Sec. 5)

Normal strain (Appendix D)

p Bending strain in the pile (Sec. 5)

Non-dimensional soil depth

Specific weight of water

Submerged specific weight of the soil

liq Specific weight of the liquefied soil

t Total specific weight of the soil

xy, yz , xz Shear deformations

Wave number

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xii Nomenclature

L Lagrange multiplier (Sec. 5)

2

Laplace operator Poissons ratio for the soil

p Poissons ratio for the pile

Angular frequency

Soil density

p Pile density

w Density of water

Normal stress

Effective stress

0

Mean initial effective stress

3

Confining pressure

p Fluctuating component of pore-water pressure

x Effective normal stress in the x-direction

z Effective normal stress in the z-direction

3,ref Reference confining pressure

x, y, z Normal stresses

Shear stress

xy, yz , xz Shear stresses

Angle (Defined in Fig. 1.2)

x+ x Effective normal stress i x-direction, normalized with the bed pore-water pressure

z+ z Effective normal stress i z-direction, normalized with the bed pore-water pressure

Non-dimensional boundary layer thickness (Sec. 4.1.2)

a Triaxial axial strain (Appendix E)

p Triaxial volume strain (Appendix E)

q Triaxial shear strain (Appendix E)

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Nomenclature xiii

r Triaxial radial strain (Appendix E)

x

, y

, z Strains

Soil friction angle

Roman Characters

< > Used to denote ensemble averaged quantities

 Ensemble averaged pore-water pressure (In excess of hydrostatic pres-sure)

C Elasticity matrix

P Period averaged pore-water pressure (In excess of hydrostatic pres-sure)

p + p Pore-water pressure normalized with the bed pore-water pressure

i, j subindex

A Constant A= 0.9 for cyclic loading (Sec. 5)

A Cross sectional area of permeameter

b A depth variableb = 0.25, 0.50, 0.75, 1.00

b Intersect between failure line and the abscissa (Appendix E)

c Effective cohesion

C1, C2, C3 Constants (Sec. 5)

CH Hazen coefficient

Cn Non-dimensional coefficients

Cp Soil resistance in non-dimension form (Sec. 5)

Cu Uniformity coefficient

cv Coefficient of consolidation

D Pile diameter

d Seabed depth in TC1

Dc Diffusion coefficient from the theory of diffusion and dispersion

Dr Relative density

ds Specific gravity of the soil grains


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xiv Nomenclature

d10 Grain size in which 10 % of the soil is finer

d50

Grain size in which 50 % of the soil is finerd60 Grain size in which 60 % of the soil is finer

E Youngs modulus of the soil

e Void ratio

ed Foundation depth

Ep Youngs modulus of the pile

ex Load eccentricity (Sec. 5)

eliq Void ratio of the liquefied soil

emax maximum void ratio

emin minimum void ratio

Epy,DNV Soil reaction modulus from DNV (2004)

Epy,num Soil reaction modulus from numerical model

Epy Reaction modulus for a pile under lateral loading (Sec. 5)

Eref Reference Youngs modulus for soilEURL Youngs modulus for the soil (unloading/reloading) (Appendix E)

F Force excerted on pile head

f Source term (Sec. 5)

Fx Volume force in x-direction

Fy Volume force in y-direction

Fz Volume force in z-direction

G Shear modulus of the soil

g Acceleration of gravity

H Wave height (Sec. 5)

h Geometric head (Appendix B)

h Water depth

HW Wave height in TC1


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Nomenclature xv

i Imaginary number

Ip Second area moment of inertiak Soil permeability

K Bulk modulus of elasticity of pore water

K0 Coefficient of lateral earth pressure

kT Modulus of subgrade reaction (Sec. 5)

Kw True bulk modulus of elasticity of water

L Distance between pressure tappings

Lc Critical length (Sec. 5)

Ls Beam span

LW Wave length in TC1

M Bending moment

m Stiffness ratio

N Normal force (Appendix D)

N Number of periodsn Soil porosity

n1, n2, n3 Normal vector components

P Pore-water pressure (In excess of hydrostatic pressure)

p Soil resistance (Sec. 5)

p0 pressure exerted on the seabed by waves

pb Amplitude of pressure exerted on the seabed by waves

Pr Raw pore-water pressure

Pmax Maximum PWP when soil is liquefied

pult Ultimate lateral soil resistance (Sec. 5)

Q Lateral force exerted by waves (Sec. 5)

Q Point load (Appendix D)

Q Water discharge


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xvi Nomenclature

q Deviator stress (Appendix E)

q Uniform loadr Distance from pile wall

r0 Pile radius

S Spreading parameter (Sec. 5)

s Strain parameter (Sec. 5)

Sr Saturation degree

st Total specific gravity of the sediment

T Period of the rocking pile

t Time

t Total time of discharge (Appendix B)

TW Wave period in TC1

tw Wall thickness of the pile (Sec. 5)

u Soil displacements in the x-direction

up pile displacements in x-directionv Soil displacements in the y-direction

VD Pile head velocity

vp pile displacements in y-direction

W Seabed width in TC1

w Soil displacements in the z-direction

wp pile displacements in z-direction

x x-coordinate

XD Displacement of the pile head

xD Amplitude of the pile head displacement

y Distance from neutral axis (Appendix D)

y Lateral displacement of the pile as function of soil depth (Sec. 5)

y y-coordinate


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Nomenclature xvii

ys Length scale

z Distance below the soil surface (Sec. 5)

z z-coordinate

zR Transition depth (Sec. 5)

Abbreviations

BCE Biot consolidation equations

EWEA European Wind Energy Association

FE Finite element

HTI Heat transfer interface

MCI Mathematics coefficient form interface

OHVS Offshore high voltage station

OWT Offshore wind turbine

PDE Partial differential equation

PWP Pore-water pressure (in excess of hydrostatic pressure)

SMI Solid mechanics interface

TC1 Test case 1


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xviii Nomenclature


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Chapter 1

Introduction

1.1 Statement of the Problem

Monopiles are presently designed according to the well-known p-y methodadopted in most design recommendations, e.g. DNV (2004). It is rarelythe ultimate lateral bearing capacity, which is the decisive factor in designof a monopile foundation. This may also be seen in the low failure rate ofmonopiles already placed in the field.

More importantly is the stiffness of the monopile foundation due to pos-sible fatigue failure. Field observations have shown that some monopiles

behaves more rigid than predicted by the current design recommendations.Therefore there is a need for better understanding of the pile / soil interactionproblem and especially the influence of various soil parameters.

1.2 Motivation of the Problem

In January 2008 the European Commission published a climate and energypackage which included the 20-20-20 targets. The targets were to cut theemission of greenhouse gases by 20 %, to cut the energy consumption by 20 %of projected 2020 levels and finally to increase the use of renewables to 20 %

of total energy production by the year 2020 (European Commission, 2008).

In year 2000 the European offshore wind energys share of the electricitydemand was 0.0 %. In year 2009 the offshore wind contributed with 0.2 % ofthe European electricity demand. The European Wind Energy Association(EWEA) forecast that the share is to increase up to 4 .3 % by year 2020 and16.7 % by year 2030 (EWEA, 2009).

Today, several options exist for foundation of an offshore wind turbine(OWT). These are the gravity-based foundation, the monopile, the tripod

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2 Chapter 1. Introduction

and the jacket type foundation. See e.g. Cuellar (2011). A new OWT foun-dation may also be mentioned, namely the bucket type foundation (Ibsen and

Liingaard, 2009). The monopile foundation is currently the preferred choiceas OWT foundation, mainly due to low production cost.

Today, monopiles of approximately 5 6 m in diameter have been in-stalled in the North Sea. At Horns Rev II, the OWT foundations were 3.9 min diameter and installed at a water depth up to 17 m. Going in deeper wa-ters, the diameter of the piles may increase up to 7.5 m in order to fulfill therequirements for sufficient bearing capacity (Achmus et al., 2009). Besidesthe requirement of sufficient bearing capacity, fatigue failure is also an im-portant aspect. Here estimates of the accumulated pile head deflection androtation, and the stiffness of the foundation are of vital importance.

Monopiles may in general be installed by one of the following three methods(DNV and Ris, 2001); 1) driving using pilling hammer where a ram isdropped on the head of the monopile, 2) driving using vibrators or 3) drivingusing drilling or excavation of seabed material. Common for all three driv-ing methods are the maximum possible pile diameter, pile length and wallthickness. At present, the largest pile possible to install in the field, usingpilling hammer method, due to limitations of driving equipment is around6 m in diameter having a length of approximately 100 m and a wall thicknessof approximately 120 mm. In addition, the transportation of the large pilediameter also implies difficulties.

Therefore there is a growing interest for better understanding of lateralloaded piles. The engineers need tools that can more accurately predict boththe long term response of a lateral loaded pile as well as the short termresponse including the stiffness of the OWT pile foundation.

1.3 Existing work

Work on lateral loaded piles have been conducted during the last hundredyears. Karl Terzaghi, who may be considered as the forefather of soil mechan-

ics started some pioneering work on laterally loaded piles and introduced thecoefficient of subgrade reaction used in the current design recommendationswhen deriving the p y curves.

The existing methods on the analysis of laterally loaded piles may be di-vided into following five groups; (1) the limit state method; (2) the subgradereaction method; (3) the p-y method; (4) the elasticity method and (5); theFinite Element Method (Fan and Long, 2005). The limit state method willnot be discussed in the content of the present work, since it is simply an equi-librium method between driving forces (lateral loads) and stabilizing forces


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1.3 Existing work 3

(passive soil resistance) as for instance in Broms (1964). Also the elasticitymethod will not be discussed.

The subgrade reaction method may also be termed the Winkler approachor the Beam on Elastic Foundation approach. It describes a method wherethe pile is assumed to be supported by a series of discrete springs, each springhaving its own spring characteristics. The behavior of each spring is assumedlinear and can be formulated as (Matlock and Reese, 1960),

p= Epyy (1.1)

where p is the soil resistance in terms of force per unit length, y is the pilelateral deflection andEpy is termed the reaction modulus and represents theslope in the p-y curve. The reaction modulus Epy may be expressed as,

Epy = kTz (1.2)

wherez is the distance below the soil surface and kTis the coefficient of sub-grade reaction, originally formulated by Terzaghi (1955). The p-y methodis a further development of the subgrade reaction method, where the linearsprings are replaced by a set of non-linear springs as in Reese et al. (1974).

The p-y method do has some shortcomings when used for design of OWTpile foundations. Among others, one of the shortcomings of the p-y methodis that it has been based on data obtained from long slender flexible piles

whereas piles installed in the field behaves more rigidly (Leblanc et al., 2010).Despite the shortcomings, the p-y method currently represents the currentstate-of-the-art for design of monopiles in the offshore industry (Leblancet al., 2010). The p-y method has been adopted in the design recommenda-tions for OWT foundations, e.g. in DNV (2004).

With the advancement of computers, finite elements models for the analy-sis of lateral loaded piles have gained more attention recent years. FE-modelsare considered as an effective tool for modelling important physics such aspile/soil interface, 3D boundary conditions and soil nonlinearity (Kim andJeong, 2011). Without any claim of being complete, some work already con-

ducted, related to the pile response from lateral loading are shortly presentedbelow.

Randolph (1981) developed a 2D finite element model for the analysis ofa lateral loaded pile. The soil was modelled as an elastic continuum and thepile was modelled as an elastic beam. Since the model was a 2D model, im-portant physics such as 3D boundary conditions could not be captured. Yangand Jeremic (2002) developed a 3D FE-model where the soil was modelled asan elasto-plastic material. The yield surface of the sand was modelled withthe Drucker-Prager yield surface and the pile was modelled as a linear-elastic


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material. The results were used to compute a set ofp y curves. The p-ycurves were obtained from static one way loading tests. Others researchers,

e.g Taha et al. (2009) modelled the soil as a Mohr-Coulomb elasto-plasticmaterial. Kim and Jeong (2011) and Zania and Hededal (2011) consideredthe soil as a Mohr-Coulomb elasto-plastic material with the non-associatedflow rule adopted. In Zania and Hededal (2011) rigid piles were consideredand the effect of friction between the pile and soil surface was investigated.Common for the preceding works, are that the soil has been modelled as amaterial without voids, hence the pore-water pressure (PWP), in excess ofhydrostatic pressure has been left out in the considerations. Therefore shortterm effects on the soil response have been left out in the preceding works.

Cuellar (2011) give a review on research work conducted in relation to

short term response arising from cyclic loading. In Cuellar (2011) a numeri-cal model with the capability of simulating the PWP in the soil during cyclicloading was developed. The model utilized the Biots consolidation equa-tions (Biot, 1941) to handle the PWP generation during cyclic loading. Themodel included a residual component to handle build-up of PWP, thus themodel had provisions to estimate the liquefaction potential for piles undercyclic loading (see e.g. Sumer and Fredse (2002) for further description ofthe liquefaction phenomena.). The model also contained a set of constitu-tive equations used to describe the stress behavior of the soil from arbitraryimposed soil deformations. However in the work by Cuellar (2011) the focuswas on the soil susceptibility to liquefaction. Taiebat (1999) also developed

a numerical model able of handling the PWP during cyclic loading. Howeverthe model was not validated against experimental test, nor was the numericalmodel used to evaluate the soil response in terms of p-y relationships.

1.4 The Niche

From the preceding review of existing work, it seems clear that numericalmodels are a viable tool to model laterally loaded piles which allows features,such as pile/soil interface, 3D boundary conditions and soil nonlinearity, to

be considered. When modelling lateral loaded piles, the equations governingthe soil behavior, are usually without a component describing the pore-waterflow. The pile is exposed to a one-way loading, thus the dynamic effect fromthe pore-water flow in the voids of the soil skeleton, is neglected. Despite thelack of the pore-water flow, the models seems to perform well when compar-ing e.g the stiffness of the foundation, with field measurements.

When it comes to poro-elastic models, able to handle the pore-water dur-ing cyclic loading, focus appears to be on soil liquefaction rather than thestiffness of the pile. In addition, calibration and validation of the models rely


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1.5 The Purpose 5

on measurements obtained from triaxial tests on soil specimens.

The niche, as it appears from the previous literature survey, is to obtainthe soil response, for full-scale conditions, including the pore-water flow andsoil stiffness by considering the soil as a linear poro-elastic material governedby the Biots consolidation equations and to validate the model using dataobtained in lab-scale experiments.

1.5 The Purpose

The purpose of the present study is to develop a numerical model simulatinga cyclic lateral loaded pile in a seabed, where the voids in the soil skeletonare filled with water. The numerical model should be able to simulate fieldconditions. The model should be based on the Biots consolidation equationscapable of handling the PWP developing during the cyclic loading of the pile.

The model should be validated against lab-scale experiments performedunder controlled conditions. Once the model is validated, it should be scaledto field conditions and soil properties normally encountered in the field,should be implemented.

The end-product of the present work, should be a parametric study, in-vestigating the influence of various parameters on the soil resistance curves(p-y curves) describing the stiffness of the pile foundation. The soil resis-tance curves should be presented in terms of the non-dimensional quantitiesdescribing the pile / soil interaction.

1.6 Methodology and Terminology

1.6.1 Methodology

In the present work, a literature study on pile / soil interaction under influ-ence of cyclic loading (Chap. 1) has been carried out. Common knowledgeand background of the pile/soil interaction problem has been gained. Based

on Biots consolidation equations, a 3D numerical model, originally describedin Jeng et al. (2010) is further developed and described (Chap. 2).

A series of experimental tests are performed in order to obtain data formodel validation (Chap. 3). In the experimental test a model pile (20 cm indiameter) is placed in a container with sand. The model pile are then movedin a cyclic fashion in order to simulate the cyclic loading of a monopile. Twoseries of tests are performed. One test on coarse sand and one on coarse silt.The PWP is measured during the cyclic loading. The coarse sand experimentis used in the model validation exercise, while the coarse silt experiment is


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for mostly academic purpose.

The numerical model is validated (Chap. 4) by 1) a simplified 2D modelwhere the PWP under progressive waves from analytical solutions is com-pared with the output from the numerical model and 2) the numerical modelis developed in 3D, and used to simulate the experimental test, and the PWPis compared.

Once the numerical model is validated, it is developed further, to simulatedfield conditions (Chap. 5). A set of non-dimensional parameters, governingthe pile / soil interaction are developed. A parametric study is performedand based on the parametric study, a set on non-dimensional soil resistancecurves are developed and the influence of the non-dimensional parameters

are investigated.

1.6.2 Terminology

To ease the reader, this small section provides an overview of the terminologyand definitions used throughout the report. In the present study an offshorepilefoundation is investigated. Pile foundations offshore are normally termedmonopile foundations. The pile foundation usually supports the tower of anoffshore wind turbine (OWT). However the pile foundation may also be usedto support other structures such as offshore high voltage structures (OHVS),e.g transformer stations. In the present report the wordingmodel pile and

pilewill be used to denote the model pile used in the experimental tests andthe pile used in the numerical simulations, respectively.

In a soil, where the voids between the soil grains are filled with water,the total stress will be composed of two parts, namely the contact stressesbetween the individual soil grains (effective stress) and the stresses from thepore-water. If the pore-water is still, the pore-water pressure (PWP) will beequal the hydrostatic pressure. However, throughout this report, the termPWP will be used to denote the pressure in the voids of the soil skeleton inexcess of hydrostatic pressure.

Finally, throughout the report words such as pile head,pile toe,pile length,foundation depth and load eccentricity will be used. Fig. 1.1 and Fig. 1.2gives a definition sketch of the terminology used.


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1.6 Methodology and Terminology 7

Figure 1.1: Definition sketch of terminology used (side view).

Figure 1.2: Definition sketch of terminology used (Plan view ).


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Chapter 2

Numerical model. Biot Equa-

tions

2.1 Introduction

This chapter will present the numerical model used in the present study. Firstthe equations governing the soil response and the pile behavior are described.The boundary conditions are presented. Then the assumptions and the lim-itations of the numerical model are discussed and finally the implementationof the equations in the commercial software package COMSOL is presented.

The basis of the numerical model was originally developed by Jeng et al.(2010) and kindly provided during the present authors visit to the UK. Anumber of modifications have been made to the original model. Originallythe numerical model included the Navier-Stokes equations to handle the wa-ter on top of the seabed. Also, the original model utilized an arbitraryLagrangian-Eulerian moving mesh in order to resolve the free surface of thewater. Both features are excluded in the present model.

Three sets of models were developed, all based on the same set of governingequations. One model, a 2D model, was used in a simple test case where theseabed response under a progressive wave was investigated. The test casewas used to validate the solution to Biots consolidation equations. A secondmodel, simulating lab-scale dimensions was developed and validated againstexperiments. Finally a full-scale model was developed, based on the lab-scale model. In the full-scale model infinite elements were used to simulatethe infinite extent of the soil.

9


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10 Chapter 2. Numerical model. Biot Equations

2.2 Governing Equations

2.2.1 The PileConsidering the pile as an elastic pile, its behavior is modelled by linearelasticity. The stress-strain relationships are given by Hookes Law,

= C (2.1)

where is the stress vector defined as,

=

xyzyzxzxy

(2.2)

where is the normal stresses, denotes the shear stresses and x, y and zrefer to the three directions in the Cartesian coordinate system (see 1.1). is the strain vector,

=

xyz

yz

xzxy

=

xyz

yz /2

xz/2

xy/2

(2.3)

Here x, y and z are the strains defined as,

x = up

x, y =

vpy

, z =wp

z (2.4)

while xy, yz and xz are the shear deformations defined as,

xy =vp

x +

upy

, yz =vp

z +

wpy

, xz = up

z +

wpx

(2.5)

where up, vp and wp are the components of the pile displacement. For

isotropic materials xy = yx, yz = zy and xz = zx because of sym-metry in the elasticity matrix C. The elasticity matrix C in Eqn. 2.1 isdefined as,

C= Ep

(1 + p)(1 2p)

1 p p p 0 0 0p 1 p p 0 0 0p p 1 p 0 0 0

0 0 0 12p

2 0 0

0 0 0 0 12p2 0

0 0 0 0 0 12p2

(2.6)


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2.2 Governing Equations 11

for an isotropic material, where Ep andp are the pile Youngs modulus andPoissons ratio respectively. The transient response of the pile, is govern by

the equations of motion, namely,

p2upt2

x

x

xyy

xz

z =Fx (2.7)

p2vpt2

yx

x

yy

yz

z =Fy (2.8)

p2wpt2

zx

x

zyy

z

z =Fz (2.9)

here p is the pile density and where Fx, Fy and Fz are the external volumeforce.

2.2.2 The Seabed

In the present study, the seabed response is assumed to be governed by theBiot consolidation equations (BCE),(Biot, 1941). The BCE have been ap-plied for a variety of applications in which the soil response is sought underdifferent types of loadings, see e.g. Ulker et al. (2012) or Jeng and Cheng(2000) for analysis of seabed instability under a caison breakwater or insta-bility of a buried pipeline, respectively.

The BCE are based on a number of assumptions by Biot (1941).

1. The soil is an isotropic material,

2. Reversibility of stress-strain relations under final equilibrium condi-tions,

3. Linearity of stress-strain relations,

4. Small strains,

5. The pore-water is incompressible,

6. The pore-water may contain air bubbles,

7. The pore-water flows through the porous media according to Darcyslaw.

When considering the soil as a poro-elastic material, the equations ofequilibrium for the soil becomes (see Sumer and Fredse (2002) or Biot (1941)for a full derivation of the equilibrium equations.),

G2u + G

1 2

x =

P

x (2.10)


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G2v+ G

1 2

y =

P

y (2.11)

G2w+ G

1 2

z =

P

z (2.12)

whereu,v andware the soil displacements,Gandare the elastic propertiesof the soil, namely the shear modulus of elasticity and the Poison ratio, P isthe PWP, 2 is the Laplacian operator and is the volume expansion,

=u

x+

v

y+

w

z (2.13)

Eq. 2.10, 2.11, and 2.12 contains four unknown, namely the soil displace-mentsu,v, wand the PWPP. Assuming that the flow of pore-water throughthe soil skeleton is governed by Darcys law coupled with the conservation ofmass of the pore-water, a fourth equation can be formulated as,

k

2P =

n

KP

t +

t (2.14)

where k is the permeability of the soil, is the specific weight of the pore-water,n is the porosity and K is the bulk modulus of the pore-water,

1

K =

1

Kw

+1 Sr

p0

(2.15)

where Kw is the true bulk modulus of water, Sr is the degree of saturationand p0 is the absolute pore-water pressure and can be taken equal to theinitial value of pressure (Sumer and Fredse, 2002). Eq. 2.14 apply for anisotropic material. The term nK

Pt in Eq. 2.14 represents the compressibi-

lity of the pore-water including the gas/air content in the water (Sumer andFredse, 2002). The equations Eq. 2.10, 2.11, and 2.12 (constitutive equa-tions) together with Eq. 2.14 (storage equation) are the Biot consolidationequations.

2.3 Boundary conditions

This section will present the boundary conditions implemented in the numer-ical models.

2.3.1 Soil in a confined Domain

In the lab-scale numerical model, the vertical walls, the slopes and the bottomof the tank (see Sec. 3) are modelled as impermeable smooth rigid walls. Thisimplies that (1) the soil at the walls is unable to move in the normal (radial)


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2.3 Boundary conditions 13

direction, but is free to move in tangential direction and (2) the flux of thePWP is null. This is expressed as follows,

n1u + n2v+ n3w= 0 (2.16)

and,

n1P

x + n2

P

y + n3

P

z = 0 (2.17)

where n= [n1, n2, n3] is the surface normal vector.

2.3.2 Soil in a unconfined Domain

For the full-scale numerical model the soil domain is modelled as if, it is ofinfinite extent. This implies that the soil displacements and the PWP attainszero value as the distance increases. Two commonly used methods of simula-ting infinite domains, are 1) model the geometry of the problem large enoughfor avoiding boundary effects, or 2) using an absorption layer (domain),where energies can be dissipated. The latter method is used in the full-scalemodel.

Infinite elements are used to simulate the infinite boundaries of the soildomain. The principle of infinite elements, is mapping from one domain to

a mapped domain. In the mapped domain, any quantity can be scaled toinfinity by a polynomial expression (Zienkiewicz et al., 1983) thus simulatinginfinite is made possible.

For the full-scale model, the soil displacements are assumed to becomezero for infinite extent and the gradient of the PWP is assumed zero. Thiscan be expressed as in Eq. 2.16 for x, y, z .

A more correct boundary as x,y , z would be that the value of PWPattains zero. However since infinite elements are used, it is considered asbeing of minor importance.

2.3.3 Pile Constraint

In the experimental tests (Sec. 3.1.1) a hinged support is used to ensure zerohorizontal displacement of the pile toe. This may simply be written as,

up = vp= wp = 0 (2.18)

Applying this constraint as a point constraint, implies rotation in that pointis allowed, meaning that the constraint acts as a hinged support.


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2.3.4 Pile displacement

The cyclic motion of the pile may be obtained in two ways, namely a forcecontrolled cyclic motion or a displacement controlled cyclic motion. Thelatter method is used throughout this thesis. In the lab-scale model, a hori-zontal displacement XD, measured in the lab-scale experiments (Sec. 3.3.1)is used as input to the displacement in the lab-scale numerical model.

For the full-scale numerical model, the pile displacement is expressed asfollows,

XD = xDsin t (2.19)

where xD being the amplitude (peak displacement) of the horizontal pile

head displacement, t being time and finally being the angular frequency,

=2

T (2.20)

where Tbeing the period of the cyclic motion. The predescribed displacementof the pile is applied as a point displacement at the pile head (see Fig. 5.5)

2.3.5 Free surface

For the mudline a free surface condition is used. This implies no constraintsof the soil displacements and no loads. A Dirichlet-type boundary condition

is used for the PWP, imposing zero PWP on the mudline.

2.3.6 Pile/soil Interface

The pile/soil interface is modelled as an impermeable no-slip interface. Thisimplies that the displacement of the soil at the pile wall, is identical to thedisplacement of the pile wall. The effect and consequence of this boundarycondition is discussed in Sec. 2.4.

2.4 Assumptions and Limitations

The present numerical model contains a number of assumptions and limita-tions. These will be presented and discussed below.

The numerical model is a poro-elastic model. This implies that all strainsin the soil is reversible. This means that the soil are unable to attain any per-manent deformation, hence features such as densification due to the cyclicshearing of the soil grains are omitted. However, since the present studyconsiders the short term response from cyclic loading, it is considered to besufficient only to model the soil as reversible. However it should be men-tioned that work, including the possible densification of the soil due to cyclic


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2.5 Implementation 15

loading, can be found in Cuellar (2011).

The numerical model does not contain any failure criteria, such as thecommonly used Mohr-Coulomb failure criterion. The consequence is, thatthe numerical model is unable to estimate the ultimate lateral resistance ofthe soil. In the present work only the stiffness of the pile foundation is con-sidered, and a failure criterion can therefore be omitted.

It is commonly known, that cyclic loading of the soil element with low per-meability (poor drainage) will cause the PWP in the soil element to build-up.This build-up is called the residual PWP. In order to obtain a residual PWP,the soil must be able to densify. The Biot equations adopted in the presentwork can not handle the build-up of PWP, hence residual PWP can not be

simulated. For instance, Jeng et al.(2010) can be consulted for a second nu-merical model, where a residual mechanism, in terms of a diffusion equationobtained from the BCE, is implemented. No attempts in the present work,on including the diffusion equation is made.

Finally, the pile/soil interface is modelled with a no-slip boundary condi-tion. As already pointed out by a number of researchers, special attentionshould be given to the pile/soil interface, e.g. Zania and Hededal (2011),Holeyman et al. (2006) and Cuellar (2011). In Grashuis et al. (1990) a de-scription of the soil behavior in a single load cycle is presented. It is stated,that during the cyclic motion of a pile, a gap forms for some portion of the

total lateral displacement y. Tensile stresses may occur due to adhesion,however these tensile stresses seems to be limited. In the present model,tensile stresses are allowed. The effect of these tensile stresses have not beeninvestigated further.

2.5 Implementation

This section describes the implementation of the numerical model in theFinite Element software COMSOL Multiphysics (ver. 4.2).

2.5.1 Features used in COMSOL

The numerical model utilizes three main physics interfaces, namely the SolidMechanics interface (SMI), and the Mathematics Coefficient form PDE (Par-tial Differential Equations) interface (MCI) or the Heat transfer interface(HTI). The equations governing the pile response (Eq. 2.1-2.9) are imple-mented in the Solid Mechanics interface.

The seabed response is implemented as follows. The three constitutiveequations (Eq. 2.10-2.12) are implemented in the SMI while the storage


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equation Eq. 2.14 is implemented in either the MCI or the HTI.

For the numerical model, simulating lab-scale conditions, the walls of thetank are considered as impermeable, which implies zero flux of PWP. Thisis equivalent to a Neumann-type boundary condition, where zero flux can bespecified. Also, in the lab-scale model, the soil is considered to be completelysaturated (See 3.1.4). For a complete saturated soil the compressibility termtends towards zero (Yamamoto et al., 1978). To model the saturated seabedresponse, the term nK

Pt in Eq. 2.14 is neglected in the numerical model.

Since the MCI allows for both specifying a Neumann-type boundary con-dition and neglecting the compressibility term, it is adopted to model thelab-scale numerical model.

For the full-scale model, the soil should be considered as an infinite soil.The MCI does not include the feature of infinite elements (COMSOL ver.4.2). Therefore, the HTI is used, since it includes infinite elements. The HTIalso allows for neglecting the compressibility term of Eq. 2.14. However itwas only possible to obtain a working model in 2D, when the compressibilityterm was neglected. It should be noted that COMSOL recently (ver. 4.2a)has included infinite elements in the MCI.

2.5.2 Special Issue with Infinite Elements

As described in Sec. 2.5.1, the full-scale numerical model includes infinite

elements. As seen from Fig. 5.4 and Fig. 5.5 (Sec. 5.3), two extra layersof soil domains are used. This is necessary, since COMSOL only allows thesame infinite elements to be used for one specific physics. Therefore one setof infinite elements is used to dissipate the PWP and a second set of infiniteelements is used to dissipate the soil displacements.

2.5.3 Computing Reaction Forces

Weak constraints were used to computed the reaction forces between the pileand the soil. When using weak constraints additional variables are computedin terms of Lagrange Multipliers, L. When applied in the SMI, L can be

interpreted as a quantity needed to satisfy a constraint. Therefore L, isequivalent to the reaction force between the pile and the soil.

2.5.4 Discretization, Analysis type and Time-scheme

For the discretization second-order Lagrange elements are used to approxi-mate the dependent variables. Transient studies (time-dependent) are usedwhen computing the soil response due to the cyclic loading. The Generalized- Method was used for time-stepping scheme. The Generalized- Method isa one-step, three stage implicit method, where accelerations, velocities and


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2.5 Implementation 17

displacements are uncoupled. The Generalized- Method is a second orderaccurate numerical scheme (Chung and Hulbert, 1993). In the numerical

model, a fixed time-step of 104

s was used to ensure convergence.

2.5.5 Hardware and Computational Time

The simulations are performed on a cluster consisting of 64 HP ProLiantSL2x170z G6 nodes. Each node consisted of two Intel Xeon Processor X5550(quad-core, 2.66GHz, 8MB L3 Cache), with 24GB of memory. The simu-lations are run on a single node in symmetric multiprocessing environment(SMP), using eight processors.

The computational time for a single computation of the full-scale model,

when simulating 20 s real-time seconds is approximately 1-2 days.


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Chapter 3

Experimental Investigation ofPile-Soil Interaction

This chapter describes the experimental tests conducted during the scope ofthis work. Two major tests were conducted. Both tests were on the investi-gation of the soil behavior during cyclic loading of a pile. The pile simulatesan OWT foundation in form of a monopile. Additionally a series of soil testswere completed in order to determine the soil properties. These tests aredescribed in appendix B, appendix C and appendix E.

The objectives with the first major test were to get an understanding of

the physical processes in the soil and to obtain data for model validation.As described in Sec. 2.4 the numerical model does not have a component tohandle build-up of PWP. As a consequence, a coarse sand (d50 = 0.65 mm)was used to ensure no build-up of PWP.

For the second major test a coarse silt was used (d50= 0.07 mm). The useof coarse silt would ensure build-up of PWP, thus the possibility of reachingliquefaction. Liquefaction may not normally be an issue during design ofOWT pile foundations because, during the installation of the pile, the soilwill be compacted. Current practiced only mention liquefaction potential inrelation to earthquake induced vibrations. However today, some consultancy

companies, consider design of OWT pile foundations without scour protec-tion as a viable option (Wittrup, 2012), meaning scour holes around the pilewill develop. These scour holes will undergo a sequence of erosion and back-fill. After backfill, the scour hole may be filled with a loose soil, thus the soilwill be susceptible to liquefaction.

For the two ma jor tests, the experimental setup was nearly similar. How-ever few changes were applied for the tests on coarse silt, including pile sup-port, testing procedure and bending moments measurements. These changeswill be described later.

19


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20 Chapter 3. Experimental Investigation of Pile-Soil Interaction

3.1 Method

3.1.1 The Experimental Setup

For the rocking pile experiment (Fig. 3.1) two cylindrical low density poly-thene tanks were used. Each tank had a volume capacity of 7 m 3. The tankdiameter was 2 m and the height was 2.63 m. The two tanks were connectedby an overflow PVC pipe placed 2.42 m from the bottom of the tank. Therocking pile experiments were conducted in only one of the tanks. This tankwill be termed Tank A. The other tank will be termed Tank B. Inside TankA, concrete slopes were established making the bottom of the tank havingthe same shape as an inverse frustum of a right circular cone.

A 243 cm long stainless steel pile was used to simulate the OWT pile foun-dation. The outer diameter of the pile was 206 mm and the wall thicknesswas 3 mm. In the case of the coarse sand experiments, the pile was supportedby a hinge connection located 7 cm from the pile toe. The hinge connectionensured zero pile displacement at the pile toe. For the coarse silt experimentsa cone fixed to the bed of Tank A was used as support. The purpose of thecone was to guide the pile to the same location when the pile was driventhrough the soil.

The rocking of the pile was performed by a conventional hydraulic piston.The piston had a load capacity of approximately 5 kN. The piston was placedon a steel tripod, bolted to the concrete floor. The force exerted at the pilehead was measured by a tension/compression S-Beam load cell having acapacity of 5 kN. The load cell was placed between the driving piston andthe pile 3 cm below the pile head.

3.1.2 Pile Displacement

To measure the pile head displacement, a potentiometer was used to measure

the displacement of the pile at the pile head. To measure the deflection alongthe length of the pile, a total of eight strain gauges were used. The straingauges were of the type single element 6 mm strain gauge. The strain gaugeswere placed 300 mm apart, starting 312 mm from the pile head (Fig. 3.1).To avoid water coming into contact with the strain gauges, the strain gaugeswere covered with ethanoic acid free silicone. To protect the silicone and thestrain gauges, a half pipe (PVC) was used to cover the entire vertical of thestrain gauges. Silicone was used as bonding and sealing material. Details onthe calibration of the strain gauges are found in appendix D.


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3.1 Method 21

Figure 3.1: Setup in Tank A used during the coarse sand tests. To keep the figuresimple, only the first vertical of the pressure rack is shown. Dimensionsshown in the unitmm.


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The pile deflection was calculated, by using the method described by Reeseand Impe (2001) and Yang and Liang (2007), namely by fitting a sixth order

polynomial to the bending moment distribution followed by a double inte-gration. The integration constants, C1 and C2 were determined using thefollowing boundary conditions,

x = XD at z= 92.5 cm (3.1)

x = 0 at z= 140.0 cm (3.2)

where x being the horizontal model pile deflection, XD being the horizontaldisplacement measured at the pile head and z being the vertical axis.

3.1.3 PWP Measurements

The PWP was measured by using Honeywell, model 26C118 15 PSI temper-ature compensated pressure transducers (Fig. 3.2). Pressure tappings, withan outer diameter of 10 mm and covered with 38 m nylon filters, were fixedon a pressure rack placed at = 0 (see Fig. 1.2). A total of 15 pressuretappings were used. The pressure tappings were arranged in five groups con-sisting of three pressure tappings with an individual vertical spacing of 2 cm.The distance between each group was 10 cm, 10 cm, 20 cm, and 45 cm . Theywere placed along three verticals with a distance r = 2 cm, r = 7 cm andr= 12 cm from the side wall of the pile (Fig. 3.3). The tubes connecting thepressure tappings to the pressure transducers were made of stainless steeltubes and transparent plastic piezometer tubes. The stainless steel tubeswere used in the soil, whereas the plastic tubes were used as connection infree space. This ensured that the pressure in the tubes would be unaffectedby pressure variations due to movement of the surrounding soil and a flexiblepressure measurements system with respect to placing the pressure rack atdifferent locations. The wall thickness of the stainless steel tubes was 1 mmand the outer diameter was 4 mm. The wall thickness of the plastic tubeswas 1 mm and the outer diameter was 4 mm. The total length of the con-nections between the pressure tappings and the pressure transducers wereapproximately 5 m. Care was taken to avoid air bubbles inside the tubes.


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3.1 Method 23

Figure 3.2: Pressure cell used for PWP measurements


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Figure 3.3: Configuration of the pressure rack used for PWP measurements.


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3.1 Method 25

Figure 3.4: Model pile.

Figure 3.5: The setup.


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Figure 3.6: Pressure rack.

Figure 3.7: Pumping system.


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3.1 Method 27

3.1.4 Seabed preparation

Prior each test, the seabed was prepared. To prepare the seabed, hydraulicbackfilling was used. Initially, the soil and water were placed in Tank B. TankA was filled with water. An overflow pipe was connecting the two tanks. Topump the mixture of soil and water from Tank B, to Tank A, a pumpingarrangement was used (Fig. 3.8). The pumping arrangement consisted ofthree submersible pumps (maximum delivery rate = 24 m3/h ). Two pumpswere used to suck a mixture of soil and water from Tank B to Tank A. Thethird pump was used to loosen the soil in Tank B by jetting water towardsthe seabed. The slurry material was ejected from the outlet of the pumpingarrangement below the water surface. The soil grains then loosely settledwith its fall velocity. This method ensured, that no air was trapped insidethe soil, hence a fully saturated seabed was likely created. A nearly identicalmethod for preparing the seabed has been reported in Rietdijk et al.(2010).

Figure 3.8: Pumping arrangement used for seabed preparation. Coarse sand setup.

The seabed preparation procedure, for the coarse sand experiments, was asfollows; (1) The model pile was installed in Tank A. (2) Tank A was filled withwater, while Tank B was filled with soil and water. (3) The three pumps wereswitched on and the pumps were lowered following the decreasing mudline.(4) When the pumps reached the bottom of Tank B, the pumping continuedfor one hour. This ensured, that only suspended sediment was left in TankB. (5) After turning off the pumps, the suspended sediment was left to settle


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in Tank A for approximately 30 minutes. (6) The water level in Tank Awas then lowered to approximately 10 cm from the mudline, by using a sub-

mersible pump. (7) The surface of the mudline was gently leveled by usinga wood plate and the distance between the pile head and the mudline wasmeasured.

For the coarse silt experiments, the procedure of preparing the seabed wasnearly identical. However, it is necessary to start from step 1. (1) Tank Awas filled with water, while Tank B was filled with soil and water. (2) Thethree pumps were switched on and the pumps were lowered following thedecreasing mudline. (3) When the pumps reached the bottom of Tank B,the pumping continued for one hour. (4) The model pile was then drivingthrough the loosely packed seabed via a guiding system down to the support

cone. (5) The suspended sediment was left to settle in Tank A for two days.(6) The water level in Tank A was then lowered to approximately 5 cm fromthe mudline making it possible to measure the distance between the pile headand the mudline. (7) Tank A was then refilled with water to the level of theoverflow pipe.

3.1.5 Visualization

In the coarse silt experiments, video recordings from the inside of the modelpile were adopted. A transparent acrylic pile with an outer diameter of200 mm was used as model pile. The model pile was placed in Tank A

prior filling the tank with soil. In this way, no soil would be inside the pile.To ensure clean water inside the model pile, the model pile was filled withclean water. To guide the video camera inside the model pile, a guidingarrangement was established. A flashlight was used to illuminate the insideof the model pile.

3.1.6 Test Conditions

This small section gives the test conditions used for both the coarse sand andthe coarse silt experiments. The test conditions for the visualization of thecoarse silt experiments are not given herein. All values correspond to initialtest conditions.The values tabulated for the pressure tappings correspond to the initial dis-tance from the pressure tapping to the mudline.


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3.1 Method 29

Unit Coarsesand

experi-ments

Coarsesilt

experi-ments

Amplitude of pile head displacement [mm] 2.4 3.3Period of cyclic loading T [s] 3 3Foundation depth ed [cm] 147 143Soil depth [cm] 154 155Water depth [cm] 10 56Pressure tapping PT 1 [cm] 0.0 0.0Pressure tapping PT 2 [cm] 0.0 0.0Pressure tapping PT 3 [cm] 0.0 0.0Pressure tapping PT 4 [cm] 1.5 1.4Pressure tapping PT 5 [cm] 3.5 3.4Pressure tapping PT 6 [cm] 5.5 5.4

Pressure tapping PT 7 [cm] 11.5 11.4Pressure tapping PT 8 [cm] 13.5 13.4Pressure tapping PT 9 [cm] 15.5 15.4Pressure tapping PT 10 [cm] 31.5 31.4Pressure tapping PT 11 [cm] 33.5 33.4Pressure tapping PT 12 [cm] 35.5 35.4Pressure tapping PT 13 [cm] 76.5 76.4Pressure tapping PT 14 [cm] 78.5 78.4Pressure tapping PT 15 [cm] 80.5 80.4

Table 3.1: Test conditions. Distances tabulated for the pressure tappings correspondto the vertical distance from the pressure tapping to the mudline.

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3.1.7 Data Treatment and Analysis

The raw data (PWP time-series) from the experiment did contain a sig-nificant amount of noise. See Appendix A for a typical unfiltered PWPtime-series. The noise consisted of both high and low frequency noise. Tofilter the data a Savitzky-Golay smoothing filter was used (Press et al., 2007).To implement the Savitzky-Golay smoothing filter a build-in matlab routinewas used. A second order k = 2 polynomial regression with a window lengthof 53 discrete data points was used.

The rocking pile experiments, may not be considered as stationary pro-cess throughout the entire experiments, since the soil properties changes withtime. But the experiments might be considered as stationary if a sufficientlysmall number of periods are considered, however the number should still belarge enough to give reliable statistical quantities.

The PWP may be analyzed in terms of a mean PWP as function of phase and may be calculated with the so-called ensemble average, which iswritten as (Sumer, 2007),

(t) = 1

N

Nj=1

P[(t + (j 1)T)] (3.3)

Likewise, the fluctuating component of the PWP as function of phase may

be defined as,

(P )2 =P =

1

N 1

Nj=1

[P[(t + (j 1)T)] (t)]2

12

(3.4)

where N being the number of periods. A sensitive analysis showed that asample N >40 was sufficient to give statistical reliable data.


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3.2 Soil Properties 31

3.2 Soil Properties

The soil used in the experimental tests were coarse sand (d50 = 0.64 mm)and coarse silt (d50 = 0.07 mm). The soil properties are presented in Tab.3.2 and Tab 3.3.

The grain size distributions (Fig. 3.9) were determined through a con-ventional sieve analysis for particles larger than or equal to 0 .063 mm. Thedistributions of particle sizes less than 0.063 mm were determined throughthe hydro-suspension method. Both methods are described in DGF Labora-toriekomite (2001).

Figure 3.9: Grain size distributions

The coarse sand and coarse silt had an uniformity coefficient (Cu= d60/d10)of 1.4 and 2.9, respectively. The coarse sand may be termed as a well sortedsoil.

The void ratio emax is when the soil is in its loosest condition and emin iswhen the soil is in its densest condition. The void ratio emax and the spe-

cific gravity of the soil grains, ds, were determined by the standard methodsprovided by the Danish Geotechnical Societys Lab Committee (DGF Lab-oratoriekomite, 2001). The minimum void ratio emin was determined byvibrating a known mixture of soil and water in a beaker until the minimumvoid ratio was reached.

For the coarse sand experiments, the initial void ratio could not be de-termined from traditional soil sampling. Instead the initial void ratio wasdetermined in the following two ways. (1) the void ratio was calculatedbased on the Tank A dimensions and the known total amount of sand in the


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tank, thus the void ratio may be considered, as a crude estimation of an av-erage void ratio. (2) the sand was gently poured down in a beaker containing

water. This should simulate the preparation of the seabed bed. The beakerwas gently tapped a few times for the soil grains to settle loosely.

To determine the void ratio for the coarse silt, the traditional soil sam-pling method was used to determine the before and after void ratios. Fromthe traditional soil sampling, only the void ratio in the upper 0 cm 20 cmcould be determined. To estimate the void ratio variation as function of soildepth, a long acrylic tube was used as a sampler. From these tests, the voidratio seemed to be slightly higher (soil being less compacted) than measuredwith the traditional sampling method. However both methods indicate thatthe soil in the coarse silt experiments may be termed as medium dense soil

(Lambe and Whitman, 1969, pg. 31). The void ratio from the traditionalsoil sampling was adopted. See appendix C for further details.

The strength- and elastic properties for the coarse sand were determinedby conducting a number of drained triaxial tests. It was found that theYoungs modulus was little influenced by the relative density Dr. An ap-proximate expression for the Youngs modulus of the coarse sand may begiven as (Appendix E),

E=Eref

33,ref

(3.5)

where Eref= 91 MPa, 3,ref= 100 kPa and = 0.61. For a stress level of1 m (3 = 9.5 kPa) the Youngs modulus for the coarse soil will be 22 MPa.Some scatter were observed when determining the Poissons ratio. An av-erage Poissons ratio of 0.20 was adopted. The friction angle was seen tovary from 40.3 (Dr = 0.50) to 44.7

(Dr = 0.80). Here a friction angle of42 was adopted. In the case of coarse silt, an Youngs modulus of 5 MPa,a Poissons ratio of 0.29 and a friction angle of 35 were adopted from thepaper of Sumer et al. (2012), since identical material was used.

A number of permeability tests on the coarse sand were conducted for

different relative densities. The permeability may be determined as,k = 0.15 Dr+ 0.45 cm/s (3.6)

Thus the coarse sand may initially be termed, a high permeable sand (k =0.37 cm/s). See appendix B for further details. The permeability coefficientfor the coarse silt was adopted from the paper of Sumer et al. (2012). Thecoarse silt may be termed as a medium permeable sand (k= 0.0015 cm/s).

It may be noticed that the degree of saturation equals unity. This impliesthat the soil do not contain any gas/air bubbles. As described in Sec. 3.1.4,


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the seabed was prepared in a way similar to what was done in Sumer et al.(1999) making it reasonable to assume that the seabed should be gas/air

bubbles free. This assumption will later be discussed in Sec. 4.2.3


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Parameter

Symbol

Value

Beforetest

Grainsize

d50

0.64mm

Specificgravityofsoil

grain

ds

2.64

Uniformitycoefficient

Cu=d60

/d10

1.4

Maximum

voidratio

emax

0.88

Minimum

voidratio

emin

0.60

Degreeofsaturation

Sr

1.00

Youngsmodulusof

elasticity

E

22MPa

Poissonsratio

0.20

Frictionangel

42

Permeability

coefficient

k

0.37cm/s

Voidratio

e

0.7

3

Porosity

n=e/(1+e)

0.4

2

Totalspecificweight

ofsediment

t=(s+e)/(1+e)w

19.

5kN/m3

Totalspecificgravity

ofsediment

st=t/w

1.9

5

Submergedspecific

weightofsediment

=t

w

9.5

kN/m3

Relativedensity

Dr=(emax

e)/(emax

em

in)

0.5

5

Table3.2:Soilproperties

,coarse

sand


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Value

Parameter

Symbol

Value

Beforetest

Aftertest

Grainsize

d50

0.07mm

Specificgravityof

soil

grain

ds

2.67

Uniformitycoefficient

Cu=d60

/d10

2.9

Maximum

voidratio

emax

1.20

Minimum

voidrat

io

emin

0.57

Degreeofsaturation

Sr

1.00

Youngsmodulusof

elasticity

E

5MPa

Poissonsratio

0.29

Frictionangel

35

Permeability

coefficient

k

0.0015cm/s

Voidratio

e

0.94

0.86

Porosity

n=e/(1+e)

0.48

0.46

Totalspecificweig

ht

ofsediment

t=(s+e)/(1+e)w

18.61kN/m

3

18.98kN/m

3

Totalspecificgrav

ity

ofsediment

st=t/w

1.86

1.90

Submergedspecific

weightofsedimen

t

=t

w

8.61kN/m

3

8.98kN/m

3

Relativedensity

Dr=(emax

e)/(emax

emin)

0.41

0.54

Table3.3:S

oilproperties,coarse

silt


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3.3 Experimental Results

3.3.1 Coarse SandThe cyclic motion of the model pile introduce cyclic shear deformations in thesoil. The cyclic shearing rearrange the soil grains. PWP will be generated dueto the reduction/expansion of the soil grains during the cyclic shearing. ThePWP generated during the cyclic loading, is governed by the Biot equations.

Pore-water Pressure during cyclic Loading

Fig. 3.10 shows the time-series of the PWP measured at PT 10. Also shown isthe associated pile head displacement and the force exerted by the hydraulicpiston. The PWP is seen to build-up initially. However, the accumulated

PWP is seen to be dissipated rapidly. This will be discussed later. From Fig.3.10.b it may be noticed that the pile head displacement decreases slightly,starting from an amplitude ofxD = 2.4 mm to xD = 1.9 mm. The decreasein amplitude is considered of minor importance. Finally, the force is seen toincrease as the rocking of the pile continues. This is expected, since the soilbecomes more compact during the cyclic loading.

Fig. 3.12 shows a close-up. (marked A in Fig. 3.10) of the time-series. Fromthe figure, the following two observations may be seen. (1) The PWP is seento build-up initially. This is indicated by defining the period average PWPP as,

P = 1

T

t+Tt

P dt (3.7)

The period averaged PWP is however quickly dissipated, which is expecteddue to the high permeability of the soil. (2) The PWP is seen to oscillatewith a frequency twice the frequency of the cyclic loading. This will be dis-cussed in a short while.

Fig. 3.13 shows another close-up (marked B in Fig. 3.10). Here it canbe seen, that the period averaged PWP has attained a constant value. It

may also be seen, that the PWP still oscillates with a frequency twice thefrequency of the cyclic loading. The explanation of the double frequency isas follows,

Considering the pile at position 1 (reference to Fig. 3.11). The pile hasmoved to its outmost position in the far field (furthers away from the pressurerack). The soil surrounding the pile is completely in contact with the pilewalls. As the pile begins to move towards the pressure tappings, the pore-water in front of the pile is pressurized (A in Fig. 3.13.a). Until position 2 isreached, the pile and the soil surrounding it, are in contact. When passing


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3.3 Experimental Results 37

A B

XD

[mm]

F

[N]

t [min]

P

[cm]

a

b

c

1

0

1

2

3

4

5

6

4

2

0

2

4

0 2 4 6 8 10 121500

1000

500

0

500

1000

1500

Figure 3.10: Time-series of coarse sand experiment. a: Pore-pressure time-series(PT 10). Measured a at vertical 2 cm from the pile and z = 31.5cmbelow the mudline. b: Pile head displacement. (+) pile motion to-wards the pressure tappings / () pile motion away from the pressuretappings. c: Applied force, (+) tension force /() compression force.


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position 2a small gap forms on the backside of the pile wall, which is filledwith pore-water (already available) and suction is generated at the backside

of the pile. This suction is felt immediately at the pressure tappings (B inFig. 3.13.a). When the pile comes to a full stop atposition 3 the PWP isdissipated and the soil grains in the meantime gradually, fill the gap. Whenthe pile move fromposition 3 toposition 4 the pore water in front of the pile(in the far field) is pressurized. This pressure is felt in the near field (C inFig. 3.13.a). When the pile passes position 4, once again, a gap is forming,this time at the pile wall in the near field. The suction associated with theformation of the gap is clearly seen in the pressure time-series (D in Fig.3.13.a). The suction is now more pronounced since the suction appears atthe near field where the pressure tappings are located. When the pile comesto a full stop at position 5, the PWP is now again dissipated. This sequence

of events concludes one period.

Figure 3.11: Illustration of pile motion, plan view

PWP generated in the soil is governed by a diffusion mechanism with adiffusion coefficient equal tocv, the coefficient of consolidation which can, toa first approximation, be estimated from (Sumer and Fredse, 2002),

cv = Gk

(3.8)

The length scale ys associated with the diffusion of the PWP may be esti-mated as (Sumer, 2007),

y2s = 2cvt (3.9)

By fixing the length scale ys to 30 cm, the time scale t for the pressure tobe sensed, can be estimated by combining Eq. 3.8 and 3.9. The time scalefound is in the order oft = O(0.015s), which is immediately.


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Finally, by comparing Fig. 3.13.a and 3.13.c it may be noticed, that thePWP and the velocity of the pile motion, are in phase. This indicates the

soil being fully saturated. This will be discussed later in Sec. 4.2.3.

Fig. 3.14 shows the PWP measured at the vertical 2 cm from the pilewall. It is seen, that the PWP measured throughout the soil depth is inphase. This also apply for the PWP measured for increasing distancer awayfrom the pile (Fig. 3.15).


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XD

[mm]

dXDdt

[mm/s]

Far field

Near field

t [s]

P

[cm]

a

b

c

P

1

0

1

2

3

4

5

6

4

2

0

2

4

0 1 2 3 4 5 6 7 8 9

6

4

2

0

2

4

6

Figure 3.12: Time-series of coarse sand experiment (Section A). a: Pore-pressuretime-series (PT 10). b: Pile head displacement. (+) pile motion to-wards the pressure tappings / () pile motion away from the pressuretappings. c: Applied force, (+) tension force /() compression force.


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XD

[mm]

dXDdt

[mm/s]

Far field

Near field

t [s]

P

[cm]

A

B

C

D

a

b

c

P

2

1.5

1

0.5

0

0.5

1

1.5

2

4

2

0

2

4

200 201 202 203 204 205 206 207 208 209

6

4

2

0

2

4

6

Pos 2

Pos 1

Pos 3

Pos 4

Pos 5

Figure 3.13: Time-series of coarse sand experiment (Section B). a: Pore-pressuretime-series (PT 10). b: Pile head displacement. (+) pile motion to-wards the pressure tappings / () pile motion away from the pressuretappings. c: Applied force, (+) tension force /() compression force.


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XD

[mm]

P

[cm]

t [s]

P

[cm]

P

[cm]

Far field

Near field

4

2

0

2

4

2

1

0

1

2

PT 7

2

1

0

1

2

PT 10

200 201 202 203 204 205 206 207 208 2092

1

0

1

2

PT 13

Figure 3.14: PWP time series measured at a vertical distance r = 2 cm, z =11.5 cm, z= 31.5 cm andz= 76.5 cm.


64/154


XD

[mm]

P

[cm]

t [s]

P

[cm]

P

[cm]

Far field

Near field

4

2

0

2

4

2

1

0

1

2

PT 10

2

1

0

1

2

PT 12

200 201 202 203 204 205 206 207 208 2092

1

0

1

2

PT 11

Figure 3.15: PWP time series measured at a horizontal distancer = 2 cm, r = 7 cmandr= 12 cm


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Vertical Pore-water Pressure Distribution

Fig. 3.16 displays the vertical PWP distribution measured at three radialdistances r at = 0. The distributions represent a snapshot in time of thePWP at phase t = 316 equivalent to the time instant of maximum PWP.Considering the magnitude of the vertical distributions, it may be noticed,that the PWP decreases as the radial distance increases. A result whichwould be expected. It shows that the generation of PWP is strongly depen-dent of the local soil displacements, since the soil displacements clearly mustdecrease when the radial distance increases.

The results also show that the PWP tends towards zero when approach-ing the mudline. This is a result which also would be expected. This meansthat although the local soil displacements increases when approaching themudline, the PWP can not obtain any increase in PWP, because PWP isdissipated instantaneously.

Finally the result also shows that the PWP decreases when approachingthe pile toe. Clearly as z approaches the pile toe, the displacements becomessmaller, thus the PWP decreases.


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Figure 3.16: Vertical pore-water pressure amplitude distributions measured at a ra-dial distance, R1 = 2 cm, R2 = 7 cm and R3 = 12 cm from the pilewall. Marks represent the point measurements. Solid line represents aeye-fit to the experimental data.


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Pile Deflection under Cyclic Loading

As described in Sec. 3.1.2, the maximum pile deflection may be obtainedfrom the bending moment distribution (Fig. 3.17.A) at phase t= /2. Asdescribed in appendix D, only four out of eight strain gauges were functioning,namely strain gauge B , C, Eand F. The final four strain gauges had to bemanually fitted to the experimental moment distribution. The procedure offitting the data from the final four strain gauges to the moment distributionis outlined in the following,

Strain gaugeA; From the pile head to the mudline, the moment distri-bution must be a straight line since moment is expressed as Moment=Forcex Arm, thus the moment must be linearly increasing from zeroat the pile head to the location of the mudline.

Strain gage D and G; The moment distribution can be represented bya 6th-order polynomial. The data points for strain gaugeD and G wereplaced such that they followed the shape of the polynomial.

Strain gauge H; At the pile toe, zero moment is expected.

After double integration of the moment distribution and utilizing the knownboundary conditions, the model pile deflection (Fig. 3.17.B) can be obtained.Also plotted in Fig. 3.17.B is the rigid pile deflection. It may be noticed thatthe deflection of the model pile is extremely small. The maximum deflectionis approxi

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